Bardzo Proszę o Pomoc Daje Naj Oblicz:a)[tex] {25}^{3} \times {0.5}^{ - 6} [/tex]b)[tex] {5}^{8} \di.... Question from @annoula

March 2022 1 9 Report

Bardzo Proszę o Pomoc Daje Naj Oblicz:
a)
[tex] {25}^{3} \times {0.5}^{ - 6} [/tex]
b)
[tex] {5}^{8} \div {0.2}^{ - 7} [/tex]
c)
[tex] \frac{ {125}^{3} \times ( {5}^{ - 2}) {}^{4} }{ {25}^{4} \times {25}^{ - 5} } [/tex]
d)
[tex] \frac{ {6}^{ - 3} \times ( {6}^{2}) {}^{ - 5} }{( \frac{1}{36} ) {}^{6} } [/tex]
e)
[tex] \frac{ ({121}^{2} ) {}^{3} }{( \frac{1}{11}) {}^{ - 8} } \times {11}^{ - 2} [/tex]
f)
[tex] \frac{ {7}^{5} \div 49}{7} \times ( \frac{1}{7} ) {}^{ - 2} [/tex]

Magda

Odpowiedź:

$a)\ \ 25^3\cdot0,5^{-6}=25^3\cdot(\frac{1}{2})^{-6}=25^3\cdot2^6=25^3\cdot2^3\cdot2^3=(25\cdot2\cdot2)^3=100^3=1000000\\\\\\b)\ \ 5^8:0,2^{-7}=5^8:(\frac{1}{5})^{-7}=5^8:5^7=5^{8-7}=5^1=5\\\\\\c)\ \ \dfrac{125^3\cdot(5^{-2})^4}{25^4\cdot25^{-5}}=\dfrac{(5^3)^3\cdot5^{-8}}{(5^2)^4\cdot(5^2)^{-5}}=\dfrac{5^9\cdot5^{-8}}{5^8\cdot5^{-10}}=\dfrac{5^{9-8}}{5^{8-10}}=\dfrac{5^1}{5^{-2}}=5^{1-(-2)}=\\\\\\=5^{1+2}=5^3=125$

$d)\ \ \dfrac{6^{-3}\cdot(6^2)^{-5}}{(\frac{1}{36})^6}=\dfrac{6^{-3}\cdot6^{-10}}{36^{-6}}=\dfrac{6^{-3-10}}{(6^2)^{-6}}=\dfrac{6^{-13}}{6^{-12}}=6^{-13-(-12)}=6^{-13+12}=\\\\\\=6^{-1}=(\frac{1}{6})^1=\frac{1}{6}\\\\\\e)\ \ \dfrac{(121^2)^3}{(\frac{1}{11})^{-8}}\cdot11^{-2}=\dfrac{121^6}{11^8}\cdot11^{-2}=\dfrac{(11^2)^6}{11^8}\cdot11^{-2}=\dfrac{11^{12}}{11^8}\cdot11^{-2}=11^{12-8}\cdot11^{-2}=\\\\\\=11^4\cdot11^{-2}=11^{4-2}=11^2=121$